Question

WebLearn Mathematice and Statistics for Manufacturing Engineers (MATH2185 1910) Student Test Page-Fourier series and DFT C 29 Question Σί,. -2injk /N k0,1,2 ..,N-1 the discrete Fourier transform is defined as: Fr= 1 0 The following nine data values are measured at evenly spaced time intervals: -0.002, 0.203, 0.303, 0.395, 0.495, 0.598, 0.699, 0.801, 0.999 For this test data, calculate the real and imaginary parts of F Maintain at least eight decimal digit accuracy throughout all your calculations. When entering your final answers you may round your estimate to five decimal digit accuracy. For example 1.673526755 or 1.67353 See the following example from MatLab. Uses the fft() command to find the discrete Fourier transform of a set of data values. y [0.5146, o.9485, 1.2788, 1.4762,1.5028,1.3101, 0.8358] tatreat (['%d'," disp (sprintf ( \nk for ic-1:length (Y) dispisprintf (fmt,ic-1, real (Y (ic)), imag (Y (ic) ))) *.'s-14.10f ,+i (.-14.1of, F(k) )) ) end F (k) +i (0.0000000000 -1.6329778499 +i(-0.0460558570) -O.3575862848 +i(-0.1442516542) -0.1417358652 +i (-0.0474369403) -0.1417358652 +i (0.0474369403 -0.3575862848 +1 (0.1442516542 -1.6329778499 +1 (0.0460558570 7.8668000000 1 2 6 Re(F1) Im(F1) Submit... Check Syntax... Previous... Test Menu... About Privacy versity- Disdaimer

format compact

format long

clear

y=[-0.003, 0.197, 0.3, 0.402, 0.496, 0.603, 0.7, 0.797, 0.996, 1.02];

Y=fft(y);

%% Display F[k]

fmt=strcat(['%d',' ','%-14.10f','+i(','%-14.10f',')']);

disp(sprintf('\nk F[k]'));

for ic=1:length(Y)

disp(sprintf(fmt,ic-1,real(Y(ic)),imag(Y(ic))));

end

%%

Answer 1

%%%%%%%%%% Matlab code %%%%%%5

clc;
close all;
clear all;
format long
y=[-0.002 0.203 0.303 0.395 0.495 0.598 0.699 0.801 0.999];
yk=fft(y);
fprintf(' Real part of F(1) = %1.5f \n' ,real(yk(2)) );
fprintf(' Imaginary part of F(1) = %1.5f \n',imag(yk(2)));

OUTPUT:

Real part of F(1) = -0.46359
Imaginary part of F(1) = 1.30059